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Table S1. Data availability, distribution and life-history traits of the species considered in the analysis. Mean length-at-age 1 was calculated from the age-length keys obtained from the DATRAS database (http://datras.ices.dk), except for plaice and sole which calculated length-at-age 1 using the von Bertalanffy equation. A50 (age at 50% maturity) values were averaged across time series and were estimated by fitting maturity ogives to sex maturity age-length keys obtained from the DATRAS database except for plaice where proportion of mature-at-age values were used. For sole, the value 2.5 was chosen as A50 is reached between age two and age three. The selectivity (age classes targeted by the fishery) values were obtained from ICES assessment working group reports and correspond to the age ranges used to estimate the average fishing mortality (F). Main preys were estimated from diet data given in Pinnegar et al. (2011) and Greenstreet (1996).

Table S2. Summary table listing the candidate factors considered to explain the synchronous decline in body size observed for a majority of substocks, their effects on body size, and the conclusions from the analyses regarding their possible links with the synchronous trend.

Table S3. Summary table of the cohorts considered as outliers for each substock, with their L values and associated standard errors (SE). Unrealistically high values of L reflect growth trajectories that are more linear than asymptotic.

Table S4. Selection table of candidate models tested in the Dynamic Factor analysis including log-likelihood, Akaike criterion (AIC) and the difference (∆AIC) between the AIC of the considered model and the best candidate model (minimum AIC observed).

Table S5. Estimated correlations between Trend 1 and the trend in density for the substocks related to Trend 1, with their corresponding P-values. The lag included in the estimation of the density is indicated (see 'Methods'). Significance was adjusted by a sequential Bonferroni correction: the ordered P-values were compared with the inequality, Pi ≤ α(1 + ki)1, Where α is the confidence level to test for significance (0.05), K is the number of correlation tests carried out and i is the rank of the correlation considered. Correlations for which the inequality is met are significant (*).

Figure S1. (a) the International Council for the Exploration of the Sea (ICES) standard round fish areas for the North Sea used for the International Bottom Trawl Surveys; (b) Overall average annual sea bottom temperature (thick continuous line) between the average of round fish areas 1 and 2 (lower continuous line) and the average of round fish areas 5 and 6 (upper continuous line). The two lower dashed lines correspond to areas 1 and 2, the two upper dashed lines to areas 5 and 6.

Figure S2. Log-scaled relationships between the K and L parameters for the substocks considered in the analysis (triangles: cod, straight crosses: haddock, circles: whiting, squares: herring, diagonal crosses: Norway pout, stars: sprat, F and M: female and male plaice, f and m (in grey): female and male sole). Filled symbols stand for substock in northern North Sea, empty symbols for substocks in the southern North Sea. Lines correspond to linear models fitted to the data points.

Figure S3. Time series of L estimates (line) with their corresponding 95% confidence intervals (shaded areas) of the thirteen substocks considered in the analysis. (a) cod North; (b) cod South; (c) haddock North; (d) whiting North; (e) whiting South; (f) herring North; (g) herring South; (h) Norway pout North; (i) sprat South; (j) male sole South; (k) female sole South; (l) male plaice South; (m) female plaice South.

Figure S4. Abundance-at-age 1 indices (filled circles) used as a proxy for density for the substocks related to Trend 1 (for both plaice and sole substocks the abundance index stands for the males and females together as no sex-specific abundance index were available) plotted along the fitted values from the best Dynamic Factor Analysis model (line) and their corresponding 95% confidence intervals [(a) haddock North; (b) Norway pout North; (c) Sprat South; (d) plaice South; (e) sole South; (f) whiting North; (g) whiting South; (h) herring North].

Figure S5. Fishing mortality (filled circles) for the substocks related to Trend 1 [fishing mortality was assumed to be equal for both male and female sole South) plotted along the fitted values from the best Dynamic Factor Analysis model (line) and their corresponding 95% confidence intervals [(a) haddock North; (b) Norway pout North; (c) Sprat South; (d) plaice South; (e) sole South; (f) whiting North; (g) whiting South; (h) herring North].

Figure S6. Mean age of each cohort (filled circles) used in estimating L for the substocks related to Trend 1 plotted along the fitted values from the best Dynamic Factor Analysis model (line) and their corresponding 95% confidence intervals [(a) haddock North; (b) Norway pout North; (c) Sprat South; (d) plaice male South; (e) sole male South; (f) sole female South; (g) whiting North; (h) whiting South; (i) herring North].

Figure S7. The common trends (black line) identified by the best-fitting Dynamic Factor Analysis (DFA) model to describe temporal variation in density (panel a), fishing mortality (panels c and e) and mean cohort age (panels g, i and k) for the eight substocks that were positively related to Trend 1 (grey line) and their corresponding factor loadings for each substock (panels b, d, f, h, j an l, respectively). For fishing mortality and mean cohort age, the best model identified by DFA included more than one trend suggesting that there is no synchrony in the fishing mortality time series and the mean age of sampled individuals for these eight substocks. For density, although the best model identified by DFA included a single trend, haddock North and sprat South did not conform to it while whiting North showed the highest factor loadings of all substocks, suggesting that the trend was mainly driven by this substock only.

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